{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Meta Labeling\n",
    "This notebook is a small MVP regarding the idea of meta labeling by Marcos Lopez de Prado, Advances in Financial Machine Learning, Chapter 3, pg 50. \n",
    "\n",
    "The central idea is to create a secondary ML model that learns how to use the primary exogenous model. This leads to improved performance metrics, including: Accuracy, Precision, Recall, and F1-Score.\n",
    "\n",
    "To illustrate the concept we made use of the MNIST data set to train a binary classifier on identifying the number 3, from a set that only includes the digits 3 and 5. The reason for this is that the number 3 looks very similar to 5 and we expect there to be some overlap in the data, i.e. the data are not linearly separable. Another reason we chose the MNIST dataset to illustrate the concept, is that MNIST is a solved problem and we can witness improvements in performance metrics with ease. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Papers\n",
    "The following papers were mentioned in the Bibliography, that highlight what we thought may have been some of the inspiration for meta labeling. \n",
    "* [Wang, J. Chan, S. 2006. Stock market trading rule discovery using two-layer bias decision tree. Expert Systems with Applications 30 (2006) 605–611 ](https://www.sciencedirect.com/science/article/pii/S095741740500148X)\n",
    "* [Qin, Q. Wang, Q. Li, J. Sam Ge, S. 2013. Linear and Nonlinear Trading Models with Gradient Boosted Random Forests and Application to Singapore Stock Market. Journal of Intelligent Learning Systems and Applications, 2013, 5, 1-10](http://file.scirp.org/pdf/JILSA_2013022213381465.pdf)\n",
    "* [Tsai, C.F. and Wang, S.P., 2009, March. Stock price forecasting by hybrid machine learning techniques. In Proceedings of the International MultiConference of Engineers and Computer Scientists (Vol. 1, No. 755, p. 60).](https://pdfs.semanticscholar.org/0fb3/9b308ec17401ec5697139dcf7f832080179f.pdf)\n",
    "* [Patel, J., Shah, S., Thakkar, P. and Kotecha, K., 2015. Predicting stock market index using fusion of machine learning techniques. Expert Systems with Applications, 42(4), pp.2162-2172.](https://www.sciencedirect.com/science/article/pii/S0957417414006551)\n",
    "* [Zhu, M., Philpotts, D., Sparks, R. and Stevenson, M.J., 2011. A hybrid approach to combining CART and logistic regression for stock ranking. Journal of Portfolio Management, 38(1), p.100.](https://search.proquest.com/openview/65025597d6bcc7b430cb9c41ddfdf203/1?pq-origsite=gscholar&cbl=49137)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advances in Financial Machine Learning, Chapter 3, page 50. Reads:\n",
    "#### Meta Labeling\n",
    "Suppose that you have a model for setting the side of the bet (long or short). You just need to learn the size of that bet, which includes the possibility of no bet at all (zero size). This is a situation that practitioners face regularly. We often know whether we want to buy or sell a product, and the only remaining question is how much money we should risk in such a bet. We do not want the ML algorithm to learn the side, just to tell us what is the appropriate size. At this point, it probably does not surprise you to hear that no book or paper has so far discussed this common problem. Thankfully, that misery ends here.\n",
    "\n",
    "I call this problem meta-labeling because we want to build a secondary ML model that learns how to use a primary exogenous model. \n",
    "\n",
    "The ML algorithm will be trained to decide whether to take the bet or pass, a purely binary prediction. When the predicted label is 1, we can use the probability of this secondary prediction to derive the size of the bet, where the side (sign) of the position has been set by the primary model.\n",
    "\n",
    "#### How to use Meta-Labeling\n",
    "Binary classification problems present a trade-off between type-I errors (false positives) and type-II errors (false negatives). In general, increasing the true positive rate of a binary classifier will tend to increase its false positive rate. The receiver operating characteristic (ROC) curve of a binary classifier measures the cost of increasing the true positive rate, in terms of accepting higher false positive rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {
      "image/png": {
       "unconfined": true,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.core.display import Image, display\n",
    "display(Image('https://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Precisionrecall.svg/660px-Precisionrecall.svg.png', width=300, unconfined=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The image illustrates the so-called “confusion matrix.” On a set of observations, there are items that exhibit a condition (positives, left rectangle), and items that do not\n",
    "exhibit a condition (negative, right rectangle). A binary classifier predicts that some items exhibit the condition (ellipse), where the TP area contains the true positives and the TN area contains the true negatives. This leads to two kinds of errors: false positives (FP) and false negatives (FN). “Precision” is the ratio between the TP area and the area in the ellipse. “Recall” is the ratio between the TP area and the area in the left rectangle. This notion of recall (aka true positive rate) is in the context of classification problems, the analogous to “power” in the context of hypothesis testing. “Accuracy” is the sum of the TP and TN areas divided by the overall set of items (square). In general, decreasing the FP area comes at a cost of increasing the FN area, because higher precision typically means fewer calls, hence lower recall. Still, there is some combination of precision and recall that maximizes the overall efficiency of the classifier. The F1-score measures the efficiency of a classifier as the harmonic average between precision and recall.\n",
    "\n",
    "**Meta-labeling is particularly helpful when you want to achieve higher F1-scores**. First, we build a model that achieves high recall, even if the precision is not particularly high. Second, we correct for the low precision by applying meta-labeling to the positives predicted by the primary model.\n",
    "\n",
    "Meta-labeling will increase your F1-score by filtering out the false positives, where the majority of positives have already been identified by the primary model. Stated differently, the role of the secondary ML algorithm is to determine whether a positive from the primary (exogenous) model is true or false. It is *not* its purpose to come up with a betting opportunity. Its purpose is to determine whether we should act or pass on the opportunity that has been presented.\n",
    "\n",
    "Meta-labeling is a very powerful tool to have in your arsenal, for four additional reasons. **First**, ML algorithms are often criticized as black boxes.\n",
    "Meta-labeling allows you to build an ML system on top of a white box (like a fundamental model founded on economic theory). This ability to transform a fundamental model into an ML model should make meta-labeling particularly useful to “quantamental” firms. **Second**, the effects of overfitting are limited when you apply metalabeling,\n",
    "because ML will not decide the side of your bet, only the size. **Third**, by decoupling the side prediction from the size prediction, meta-labeling enables sophisticated\n",
    "strategy structures. For instance, consider that the features driving a rally may differ from the features driving a sell-off. In that case, you may want to develop an\n",
    "ML strategy exclusively for long positions, based on the buy recommendations of a primary model, and an ML strategy exclusively for short positions, based on the\n",
    "sell recommendations of an entirely different primary model. **Fourth**, achieving high accuracy on small bets and low accuracy on large bets will ruin you. As important as\n",
    "identifying good opportunities is to size them properly, so it makes sense to develop an ML algorithm solely focused on getting that critical decision (sizing) right. We will\n",
    "retake this fourth point in Chapter 10. In my experience, meta-labeling ML models can deliver more robust and reliable outcomes than standard labeling models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='MNIST.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Architecture\n",
    "The following image explains the model architecture. The **first** step is to train a primary model (binary classification). **Second** a threshold level is determined at which the primary model has a high recall, in the coded example you will find that 0.30 is a good threshold, ROC curves could be used to help determine a good level. **Third** the features from the first model are concatenated with the predictions from the first model, into a new feature set for the secondary model. Meta Labels are used as the target variable in the second model. Now fit the second model. **Fourth** the prediction from the secondary model is combined with the prediction from the primary model and only where both are true, is your final prediction true. I.e. if your primary model predicts a 3 and your secondary model says you have a high probability of the primary model being correct, is your final prediction a 3, else not 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='Model Architecture.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# MVP Using MNIST Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import libraries needed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "import itertools\n",
    "import seaborn as sns\n",
    "from subprocess import check_output\n",
    "from sklearn import metrics as sk_metrics\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "import keras\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Flatten, Conv2D, MaxPool2D\n",
    "from keras.utils import to_categorical\n",
    "from keras.layers.normalization import BatchNormalization\n",
    "from keras.preprocessing.image import ImageDataGenerator\n",
    "from keras.callbacks import ReduceLROnPlateau\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Functions:\n",
    "Two functions are specified. The first to plot ROC curves and give an indication at which level to set the thresholds. Second to compare the results of modeling without and then with meta labeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_roc(actual, prediction):\n",
    "    # Calculate ROC / AUC\n",
    "    fpr, tpr, thresholds = sk_metrics.roc_curve(actual, prediction, pos_label=1)\n",
    "    roc_auc = sk_metrics.auc(fpr, tpr)\n",
    "\n",
    "    # Plot\n",
    "    plt.plot(fpr, tpr, color='darkorange',\n",
    "             lw=2, label='ROC curve (area = %0.2f)' % roc_auc)\n",
    "    plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n",
    "    plt.xlim([0.0, 1.0])\n",
    "    plt.ylim([0.0, 1.05])\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "    plt.title('Receiver Operating Characteristic Example')\n",
    "    plt.legend(loc=\"lower right\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_meta_label(primary_model, secondary_model, x, y, threshold):\n",
    "    \"\"\"\n",
    "    Function outputs the results of the primary model with a threshold of 50%. It then outputs the results of the meta model.\n",
    "    Ideally you want to see that the meta model out performs the primary model.\n",
    "\n",
    "    I am busy investigating why meta modeling works. A little tricky since I'm yet to find a solid paper on the technique. Its very briefly mentioned in\n",
    "    Advances in Financial Machine Learning.\n",
    "\n",
    "    :param primary_model: model object (First, we build a model that achieves high recall, even if the precision is not particularly high)\n",
    "    :param secondary_model: model object (the role of the secondary ML algorithm is to determine whether a positive from the primary (exogenous) model\n",
    "                            is true or false. It is not its purpose to come up with a betting opportunity. Its purpose is to determine whether\n",
    "                            we should act or pass on the opportunity that has been presented.)\n",
    "    :param x: Explanatory variables\n",
    "    :param y: Target variable (One hot encoded)\n",
    "    :param threshold: The confidence threshold. This is used\n",
    "    :return: Print the classification report for both the base model and the meta model.\n",
    "    \"\"\"\n",
    "    # Get the actual labels (y) from the encoded y labels\n",
    "    actual = np.array([i[1] for i in y]) == 1\n",
    "\n",
    "    # Use primary model to score the data x\n",
    "    primary_prediction = primary_model.predict(x)\n",
    "    primary_prediction = np.array([i[1] for i in primary_prediction]).reshape((-1, 1))\n",
    "    primary_prediction_int = primary_prediction > threshold # binary labels\n",
    "\n",
    "    # Print output for base model\n",
    "    print('Base Model Metrics:')\n",
    "    print(sk_metrics.classification_report(actual, primary_prediction > 0.50))\n",
    "    print('Confusion Matrix')\n",
    "    print(sk_metrics.confusion_matrix(actual, primary_prediction_int))\n",
    "    accuracy = (actual == primary_prediction_int.flatten()).sum() / actual.shape[0]\n",
    "    print('Accuracy: ', round(accuracy, 4))\n",
    "    print('')\n",
    "\n",
    "    # Secondary model\n",
    "    new_features = np.concatenate((primary_prediction_int, x), axis=1)\n",
    "\n",
    "    # Use secondary model to score the new features\n",
    "    meta_prediction = secondary_model.predict(new_features)\n",
    "    meta_prediction = np.array([i[1] for i in meta_prediction])\n",
    "    meta_prediction_int = meta_prediction > 0.5 # binary labels\n",
    "\n",
    "    # Now combine primary and secondary model in a final prediction\n",
    "    final_prediction = (meta_prediction_int & primary_prediction_int.flatten())\n",
    "\n",
    "    # Print output for meta model\n",
    "    print('Meta Label Metrics: ')\n",
    "    print(sk_metrics.classification_report(actual, final_prediction))\n",
    "    print('Confusion Matrix')\n",
    "    print(sk_metrics.confusion_matrix(actual, final_prediction))\n",
    "    accuracy = (actual == final_prediction).sum() / actual.shape[0]\n",
    "    print('Accuracy: ', round(accuracy, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Exploration\n",
    "Download the MNIST data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({7: 1028,\n",
       "         2: 1032,\n",
       "         1: 1135,\n",
       "         0: 980,\n",
       "         4: 982,\n",
       "         9: 1009,\n",
       "         5: 892,\n",
       "         6: 958,\n",
       "         3: 1010,\n",
       "         8: 974})"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show the counts of each number\n",
    "Counter(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the distribution of numbers\n",
    "sns.countplot(y_test)\n",
    "plt.title('Distribution of Images')\n",
    "plt.xlabel('Images')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Normalize and Subset Data\n",
    "* It is standard practice to normalize the MNIST data by 255.0\n",
    "* Next we subset the data so that we only include the numbers 3 and 5\n",
    "* Reshape the data: We will use a feed forward neural network or a logistic regression, for this we can just flatten the images\n",
    "* One Hot Encode the target variables\n",
    "* Do a test train split, keep a hold out sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalising the data\n",
    "x_train = x_train / 255.0\n",
    "x_test = x_test / 255.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X values\n",
      "x_train (11552, 28, 28)\n",
      "x_test (1902, 28, 28) \n",
      "\n",
      "Y values\n",
      "y train (11552,)\n",
      "y test (1902,)\n"
     ]
    }
   ],
   "source": [
    "# Change these params if you want to change the numbers selected\n",
    "num1 = 3\n",
    "num2 = 5\n",
    "\n",
    "# Subset on only two numbers\n",
    "x_sub_train = x_train[(y_train == num1) | (y_train == num2)]\n",
    "y_sub_train = y_train[(y_train == num1) | (y_train == num2)]\n",
    "\n",
    "x_sub_test = x_test[(y_test == num1) | (y_test == num2)]\n",
    "y_sub_test = y_test[(y_test == num1) | (y_test == num2)]\n",
    "\n",
    "print('X values')\n",
    "print('x_train', x_sub_train.shape)\n",
    "print('x_test', x_sub_test.shape, '\\n')\n",
    "print('Y values')\n",
    "print('y train', y_sub_train.shape)\n",
    "print('y test', y_sub_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Flatten input\n",
    "x_train_flat = x_sub_train.flatten().reshape(x_sub_train.shape[0], 28*28)\n",
    "x_test_flat = x_sub_test.flatten().reshape(x_sub_test.shape[0], 28*28)\n",
    "\n",
    "# One hot encode target variables\n",
    "y_sub_train_encoded = to_categorical([1 if value == num1 else 0 for value in y_sub_train])\n",
    "\n",
    "# Test train split\n",
    "X_train, X_val, Y_train, Y_val = train_test_split(x_train_flat, y_sub_train_encoded, test_size = 0.1, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Build Primary Model with High Recall\n",
    "The **first** step is to train a primary model (binary classification). For this we trained a logistic regression, using the keras package. The data are split into a 90% train, 10% validation. This allows us to see when we are overfitting.\n",
    "* Loss function: categorical crossentropy \n",
    "* Optimizer: Adam ([Keras Optimizers](https://keras.io/optimizers/))\n",
    "* Epochs: 3\n",
    "* Batch size: 320\n",
    "\n",
    "You can train a more complex neural network by adding more dense layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 10396 samples, validate on 1156 samples\n",
      "Epoch 1/3\n",
      "10396/10396 [==============================] - 1s 48us/step - loss: 0.4704 - acc: 0.8121 - val_loss: 0.3416 - val_acc: 0.8988\n",
      "Epoch 2/3\n",
      "10396/10396 [==============================] - 0s 26us/step - loss: 0.2904 - acc: 0.9188 - val_loss: 0.2546 - val_acc: 0.9230\n",
      "Epoch 3/3\n",
      "10396/10396 [==============================] - 0s 22us/step - loss: 0.2283 - acc: 0.9335 - val_loss: 0.2179 - val_acc: 0.9325\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f55fcf0eb70>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build primary model\n",
    "model = Sequential()\n",
    "model.add(Dense(units=2, activation='softmax'))\n",
    "\n",
    "model.compile(loss='categorical_crossentropy',\n",
    "              optimizer='adam',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x=X_train, y=Y_train, validation_data=(X_val, Y_val), epochs=3, batch_size=320) # batch size is so large so that the model can be poorly fit, Its easy to get 99% accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Second** a threshold level is determined at which the primary model has a high recall, in the coded example you will find that 0.30 is a good threshold, ROC curves could be used to help determine a good level. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot ROC\n",
    "prediction = model.predict(X_train)\n",
    "prediction = np.array([i[1] for i in prediction])\n",
    "actual = np.array([i[1] for i in Y_train]) == 1\n",
    "\n",
    "plot_roc(actual, prediction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.98      0.79      0.87      4861\n",
      "        True       0.84      0.99      0.91      5535\n",
      "\n",
      "   micro avg       0.89      0.89      0.89     10396\n",
      "   macro avg       0.91      0.89      0.89     10396\n",
      "weighted avg       0.91      0.89      0.89     10396\n",
      "\n",
      "Confusion Matrix\n",
      "[[3817 1044]\n",
      " [  76 5459]]\n"
     ]
    }
   ],
   "source": [
    "# Create a model with high recall, change the threshold until a good recall level is reached\n",
    "threshold = .30\n",
    "prediction_int = np.array(prediction) > threshold\n",
    "\n",
    "# Classification report\n",
    "print(sk_metrics.classification_report(actual, prediction_int))\n",
    "\n",
    "# Confusion matrix\n",
    "cm = sk_metrics.confusion_matrix(actual, prediction_int)\n",
    "print('Confusion Matrix')\n",
    "print(cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that by increasing our true positive rate (Recall) we have also increased our false positive rate. You are encouraged to change the threshold levels to see how it impacts on Recall."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build Meta Model\n",
    "**Third** the features from the first model are concatenated with the predictions from the first model, into a new feature set for the secondary model. Meta Labels are used as the target variable in the second model. Now fit the second model.\n",
    "\n",
    "Meta labels are defined as: If the primary model's predictions matches the actual values, then we label it as 1, else 0. In the code below we said that if an observation was a true positive or true negative then label it as 1(i.e. the model is correct), else 0 (the model in incorrect). Note that because it is categorical, we have to add One Hot Encoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get meta labels\n",
    "meta_labels = prediction_int & actual\n",
    "meta_labels_encoded = to_categorical(meta_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reshape data\n",
    "prediction_int = prediction_int.reshape((-1, 1))\n",
    "\n",
    "# MNIST data + forecasts_int\n",
    "new_features = np.concatenate((prediction_int, X_train), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use logistic regression here as well. We could have used a more complicated model but it turns out that it's very easy to differentiate between 2 numbers of MNIST data. So we used a simple model to make sure we get a model that leaves room for improvement. \n",
    "* Loss function: categorical crossentropy \n",
    "* Optimizer: Adam ([Keras Optimizers](https://keras.io/optimizers/))\n",
    "* Epochs: 4\n",
    "* Batch size: 32\n",
    "\n",
    "You can train a more complex neural network by adding more dense layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/4\n",
      "10396/10396 [==============================] - 1s 101us/step - loss: 0.2552 - acc: 0.9024\n",
      "Epoch 2/4\n",
      "10396/10396 [==============================] - 1s 92us/step - loss: 0.1269 - acc: 0.9538\n",
      "Epoch 3/4\n",
      "10396/10396 [==============================] - 1s 73us/step - loss: 0.1060 - acc: 0.9620\n",
      "Epoch 4/4\n",
      "10396/10396 [==============================] - 1s 84us/step - loss: 0.0961 - acc: 0.9643\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f55fd640828>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train a new model \n",
    "# Build model\n",
    "meta_model = Sequential()\n",
    "meta_model.add(Dense(units=2, activation='softmax'))\n",
    "\n",
    "meta_model.compile(loss='categorical_crossentropy',\n",
    "              optimizer='adam',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "# x_train and y_train are Numpy arrays --just like in the Scikit-Learn API.\n",
    "meta_model.fit(x=new_features, y=meta_labels_encoded, epochs=4, batch_size=32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Evaluate Performance\n",
    "**Fourth** the prediction from the secondary model is combined with the prediction from the primary model and only where both are true, is your final prediction true. e.g. if your primary model predicts a 3 and your secondary model says you have a high probability of the primary model being correct, is your final prediction a 3, else not 3.\n",
    "\n",
    "The section below shows the performance of the primary model vs the performance of using meta labeling. Notice how the performance metrics improve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate train data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base Model Metrics:\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.94      0.92      0.93      4861\n",
      "        True       0.93      0.95      0.94      5535\n",
      "\n",
      "   micro avg       0.94      0.94      0.94     10396\n",
      "   macro avg       0.94      0.94      0.94     10396\n",
      "weighted avg       0.94      0.94      0.94     10396\n",
      "\n",
      "Confusion Matrix\n",
      "[[3817 1044]\n",
      " [  76 5459]]\n",
      "Accuracy:  0.8923\n",
      "\n",
      "Meta Label Metrics: \n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.94      0.97      0.96      4861\n",
      "        True       0.97      0.95      0.96      5535\n",
      "\n",
      "   micro avg       0.96      0.96      0.96     10396\n",
      "   macro avg       0.96      0.96      0.96     10396\n",
      "weighted avg       0.96      0.96      0.96     10396\n",
      "\n",
      "Confusion Matrix\n",
      "[[4704  157]\n",
      " [ 274 5261]]\n",
      "Accuracy:  0.9585\n"
     ]
    }
   ],
   "source": [
    "test_meta_label(primary_model=model, secondary_model=meta_model, x=X_train, y=Y_train, threshold=threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Evaluate validation Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base Model Metrics:\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.94      0.93      0.93       560\n",
      "        True       0.93      0.94      0.93       596\n",
      "\n",
      "   micro avg       0.93      0.93      0.93      1156\n",
      "   macro avg       0.93      0.93      0.93      1156\n",
      "weighted avg       0.93      0.93      0.93      1156\n",
      "\n",
      "Confusion Matrix\n",
      "[[428 132]\n",
      " [ 13 583]]\n",
      "Accuracy:  0.8746\n",
      "\n",
      "Meta Label Metrics: \n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.94      0.96      0.95       560\n",
      "        True       0.97      0.94      0.95       596\n",
      "\n",
      "   micro avg       0.95      0.95      0.95      1156\n",
      "   macro avg       0.95      0.95      0.95      1156\n",
      "weighted avg       0.95      0.95      0.95      1156\n",
      "\n",
      "Confusion Matrix\n",
      "[[540  20]\n",
      " [ 35 561]]\n",
      "Accuracy:  0.9524\n"
     ]
    }
   ],
   "source": [
    "test_meta_label(primary_model=model, secondary_model=meta_model, x=X_val, y=Y_val, threshold=threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Evaluate hold out sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Flatten input\n",
    "x_test_flat = x_sub_test.flatten().reshape(x_sub_test.shape[0], 28*28)\n",
    "\n",
    "# One hot encode target variables\n",
    "y_sub_test_encoded = to_categorical([1 if value == num1 else 0 for value in y_sub_test])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Base Model Metrics:\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.95      0.94      0.94       892\n",
      "        True       0.94      0.96      0.95      1010\n",
      "\n",
      "   micro avg       0.95      0.95      0.95      1902\n",
      "   macro avg       0.95      0.95      0.95      1902\n",
      "weighted avg       0.95      0.95      0.95      1902\n",
      "\n",
      "Confusion Matrix\n",
      "[[700 192]\n",
      " [ 11 999]]\n",
      "Accuracy:  0.8933\n",
      "\n",
      "Meta Label Metrics: \n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.95      0.96      0.95       892\n",
      "        True       0.96      0.95      0.96      1010\n",
      "\n",
      "   micro avg       0.96      0.96      0.96      1902\n",
      "   macro avg       0.96      0.96      0.96      1902\n",
      "weighted avg       0.96      0.96      0.96      1902\n",
      "\n",
      "Confusion Matrix\n",
      "[[857  35]\n",
      " [ 47 963]]\n",
      "Accuracy:  0.9569\n"
     ]
    }
   ],
   "source": [
    "test_meta_label(primary_model=model, secondary_model=meta_model, x=x_test_flat, y=y_sub_test_encoded, threshold=threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Conclusion\n",
    "Meta labeling works as advertised.\n",
    "\n",
    "We can see that in the confusion matrix, that the false positives from the primary model, are now being correctly identified as true negatives with the help of meta labeling. This leads to a boost in performance metrics."
   ]
  }
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